i-form

Bolzano himself identifies explicitly the form of a proposition with a set of propositions (WL I, 48, WL II, 82): The form of a proposition s with respect to a sequence i of ideas or (as an abbreviation) the i-form of s is the set of all i-variants of s, provided that at least one of the ik™s is contained in

Slices of Matisse gerard varni 2009

A propositional i-form can therefore be defined as the i-form of at least one proposition s; and a propositional form is a propositional i-form with respect to at least one sequence i.

Slices of Matisse gerard varni 2009

(For cases in which this proviso is not met, neither an i-variant of s nor the i-form of s is defined.)

Slices of Matisse gerard varni 2009

A proposition s is universally valid (or universally contravalid, respectively) with respect to a sequence i of ideas iff there is a propositional form F such that F is a propositional i-form which is universally valid (or contravalid, respectively), and s is a member of F.

Slices of Matisse gerard varni 2009